Chapter 7.7, Problem 7.90ACB

Oil content of fried sweet potato chips. Refer to the Journal of Food Engineering (September 2013) study of the characteristics of sweet potato chips fried at different temperatures, Exercise 6.9719 (p. 347). Recall that a sample of 6 sweet potato slices were fried at 130° using a vacuum fryer, and the internal oil content (gigagrams [Gg]) was measured for each slice. The results were: $\bar{x}=.178\text{Gg}$ and s =. 011 Gg.

1. a. Conduct a test of hypothesis to determine if the standard deviation, , of the population of internal oil contents for sweet potato slices fried at 130° differs from .1. Use α = .05.
2. b. In Exercise 6.97, you formed a 95% confidence interval for the true standard deviation of the internal oil content distribution for the sweet potato chips. Use this interval to make an inference about whether σ = .1. Does the result agree with the test, part a?

6.97 Oil content of fried sweet potato chips. The characteristics of sweet potato chips fried at different temperatures were investigated in the Journal of Food Engineering (September 2013). A sample of 6 sweet potato slices were fried at 130° using a vacuum fryer. One characteristic of interest to the researchers was internal oil content (measured in millions of grams). The results were: $\bar{x}=178$ and s = 11. The researchers are interested in estimating the variance of the interval oil content measurements for sweet potato chips.

1. a. Identify the target parameter, in symbols and words.
2. b. Compute a 95% confidence interval for σ².
3. c. What does it mean to say that the target parameter lies within the interval with “95% confidence”?
4. d. What assumption about the data must be satisfied in order for the confidence interval to be valid?
5. e. To obtain a practical interpretation of the interval, part b, explain why a confidence interval for the standard deviation, σ, is desired.
6. f. Use the results, part b, to compute a 95% confidence interval for σ. Give a practical interpretation of the interval.